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During the summer, Jody earns [tex]$\$[/tex]10[tex]$ per hour babysitting and $[/tex]\[tex]$15$[/tex] per hour doing yard work. This week she worked 34 hours and earned [tex]$\$[/tex]410[tex]$. If $[/tex]x[tex]$ represents the number of hours she babysat and $[/tex]y$ represents the number of hours she did yard work, which system of equations models this situation?

A. [tex]$x + y = 34$[/tex]
[tex]$10x + 15y = 410$[/tex]

B. [tex]$x + y = 410$[/tex]
[tex]$10x + 15y = 34$[/tex]

C. [tex]$x + y = 34$[/tex]
[tex]$15x + 10y = 410$[/tex]

D. [tex]$x + y = 410$[/tex]
[tex]$15x + 10y = 34$[/tex]

Sagot :

GinnyAnsweridn
In this problem, we need to find the correct system of linear equations that models the given situation about Jody's work hours and earnings.

Let's start by defining the variables:
- \( x \): the number of hours Jody babysat.
- \( y \): the number of hours Jody did yardwork.

According to the problem, Jody worked a total of 34 hours. This gives us the first equation:
[tex]\[ x + y = 34 \][/tex]

Next, we know that Jody earns \[tex]$10 per hour babysitting and \$[/tex]15 per hour doing yardwork. This week, she earned a total of \$410. Thus, we can write the second equation based on her earnings:
[tex]\[ 10x + 15y = 410 \][/tex]

Now, we need to identify the system of equations from the given options:

### Option A
[tex]\[ x + y = 34 \][/tex]
[tex]\[ 10x + 15y = 410 \][/tex]

### Option B
[tex]\[ x + y = 410 \][/tex]
[tex]\[ 10x + 15y = 34 \][/tex]

### Option C
[tex]\[ x + y = 34 \][/tex]
[tex]\[ 15x + 10y = 410 \][/tex]

### Option D
[tex]\[ x + y = 410 \][/tex]
[tex]\[ 15x + 10y = 34 \][/tex]

Comparing each option to our formulated system of equations:

- Option A has the system:
[tex]\[ x + y = 34 \][/tex]
[tex]\[ 10x + 15y = 410 \][/tex]
Which matches our equations.

- Option B has the system:
[tex]\[ x + y = 410 \][/tex]
[tex]\[ 10x + 15y = 34 \][/tex]
Which does not match our equations.

- Option C has the system:
[tex]\[ x + y = 34 \][/tex]
[tex]\[ 15x + 10y = 410 \][/tex]
Which has the coefficients of \( x \) and \( y \) swapped in the second equation. Therefore, it does not match.

- Option D has the system:
[tex]\[ x + y = 410 \][/tex]
[tex]\[ 15x + 10y = 34 \][/tex]
Which does not match our equations.

Based on our comparisons, Option A is the correct system of equations that models the situation.

Therefore, the correct answer is:
[tex]\[ \boxed{1} \][/tex]
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